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      Some estimates of precision of the Cusa-Huygens approximation

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          Abstract

          In this paper we present some new upper bounds of Cusa-Huygens approximation and obtain the corresponding two bilateral inequalities which improved Zhu's results which relate to Frame's inequalities.

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          Refinements, Generalizations, and Applications of Jordan's Inequality and Related Problems

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            A source of inequalities for circular functions

            Ling Zhu (2009)
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              The natural algorithmic approach of mixed trigonometric-polynomial problems

              The aim of this paper is to present a new algorithm for proving mixed trigonometric-polynomial inequalities of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}
              \begin{document}$$\sum_{i=1}^{n}\alpha _{i}x^{p_{i}} \cos ^{q_{i}} x\sin ^{r_{i}} x>0 $$\end{document}
              ∑ i = 1 n α i x p i cos q i x sin r i x > 0 by reducing them to polynomial inequalities. Finally, we show the great applicability of this algorithm and, as an example, we use it to analyze some new rational (Padé) approximations of the function cos2 x and to improve a class of inequalities by Yang. The results of our analysis could be implemented by means of an automated proof assistant, so our work is a contribution to the library of automatic support tools for proving various analytic inequalities.
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                Author and article information

                Journal
                27 June 2019
                Article
                1907.00712
                50ee7df5-8c91-430a-bfdc-691185379ac2

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                math.GM

                General mathematics
                General mathematics

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